A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. Based on this information, the predicted mean weekly spending for a student with a weekly income of $225 would be ____________ dollars.
Question
A consumer's spending is widely believed to be a function of their income. To estimate this relationship, a university professor randomly selected 19 of his students and collected information on their spending (Y, in dollars) and income (X, in dollars) patterns in week 6 of the semester. Assuming a linear relationship between Y and X, the professor used the least-squares method and found that the Y intercept = 20.90 and the slope = 0.66. Based on this information, the predicted mean weekly spending for a student with a weekly income of $225 would be ____________ dollars.
Solution
Answer: To predict the mean weekly spending for a student with a weekly income of $225, we substitute X = 225 into the regression equation Y = b0 + b1X.
So, Y = 20.90 + 0.66(225) = 168.90
This means that for a student with a weekly income of 168.90.
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